Properties

Label 114.4.e.d.49.2
Level $114$
Weight $4$
Character 114.49
Analytic conductor $6.726$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 114.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.72621774065\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.627014547.1
Defining polynomial: \(x^{6} + 26 x^{4} + 169 x^{2} + 147\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 49.2
Root \(4.00355i\) of defining polynomial
Character \(\chi\) \(=\) 114.49
Dual form 114.4.e.d.7.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.09405 + 3.62701i) q^{5} +(3.00000 + 5.19615i) q^{6} +3.18810 q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-2.09405 + 3.62701i) q^{5} +(3.00000 + 5.19615i) q^{6} +3.18810 q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-4.18810 - 7.25401i) q^{10} +69.4003 q^{11} -12.0000 q^{12} +(4.06431 + 7.03960i) q^{13} +(-3.18810 + 5.52196i) q^{14} +(6.28216 + 10.8810i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(53.0418 - 91.8711i) q^{17} +18.0000 q^{18} +(42.6656 - 70.9834i) q^{19} +16.7524 q^{20} +(4.78216 - 8.28294i) q^{21} +(-69.4003 + 120.205i) q^{22} +(88.2468 + 152.848i) q^{23} +(12.0000 - 20.7846i) q^{24} +(53.7299 + 93.0629i) q^{25} -16.2573 q^{26} -27.0000 q^{27} +(-6.37621 - 11.0439i) q^{28} +(33.1109 + 57.3498i) q^{29} -25.1286 q^{30} -140.915 q^{31} +(-16.0000 - 27.7128i) q^{32} +(104.100 - 180.307i) q^{33} +(106.084 + 183.742i) q^{34} +(-6.67606 + 11.5633i) q^{35} +(-18.0000 + 31.1769i) q^{36} -156.003 q^{37} +(80.2814 + 144.882i) q^{38} +24.3859 q^{39} +(-16.7524 + 29.0160i) q^{40} +(207.281 - 359.022i) q^{41} +(9.56431 + 16.5659i) q^{42} +(-57.9252 + 100.329i) q^{43} +(-138.801 - 240.410i) q^{44} +37.6929 q^{45} -352.987 q^{46} +(-310.141 - 537.181i) q^{47} +(24.0000 + 41.5692i) q^{48} -332.836 q^{49} -214.920 q^{50} +(-159.125 - 275.613i) q^{51} +(16.2573 - 28.1584i) q^{52} +(185.993 + 322.149i) q^{53} +(27.0000 - 46.7654i) q^{54} +(-145.328 + 251.715i) q^{55} +25.5048 q^{56} +(-120.422 - 217.324i) q^{57} -132.444 q^{58} +(-45.8465 + 79.4084i) q^{59} +(25.1286 - 43.5241i) q^{60} +(-109.310 - 189.331i) q^{61} +(140.915 - 244.072i) q^{62} +(-14.3465 - 24.8488i) q^{63} +64.0000 q^{64} -34.0436 q^{65} +(208.201 + 360.615i) q^{66} +(72.6712 + 125.870i) q^{67} -424.334 q^{68} +529.481 q^{69} +(-13.3521 - 23.1265i) q^{70} +(-443.915 + 768.883i) q^{71} +(-36.0000 - 62.3538i) q^{72} +(-99.5081 + 172.353i) q^{73} +(156.003 - 270.205i) q^{74} +322.379 q^{75} +(-331.225 - 5.83100i) q^{76} +221.255 q^{77} +(-24.3859 + 42.2376i) q^{78} +(194.779 - 337.367i) q^{79} +(-33.5048 - 58.0321i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(414.563 + 718.044i) q^{82} +380.039 q^{83} -38.2573 q^{84} +(222.145 + 384.766i) q^{85} +(-115.850 - 200.659i) q^{86} +198.666 q^{87} +555.202 q^{88} +(212.899 + 368.753i) q^{89} +(-37.6929 + 65.2861i) q^{90} +(12.9575 + 22.4430i) q^{91} +(352.987 - 611.392i) q^{92} +(-211.372 + 366.107i) q^{93} +1240.57 q^{94} +(168.113 + 303.391i) q^{95} -96.0000 q^{96} +(-209.923 + 363.597i) q^{97} +(332.836 - 576.489i) q^{98} +(-312.301 - 540.922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} + O(q^{10}) \) \( 6 q - 6 q^{2} + 9 q^{3} - 12 q^{4} - 10 q^{5} + 18 q^{6} + 14 q^{7} + 48 q^{8} - 27 q^{9} - 20 q^{10} - 88 q^{11} - 72 q^{12} + 9 q^{13} - 14 q^{14} + 30 q^{15} - 48 q^{16} + 84 q^{17} + 108 q^{18} + 32 q^{19} + 80 q^{20} + 21 q^{21} + 88 q^{22} + 2 q^{23} + 72 q^{24} + 83 q^{25} - 36 q^{26} - 162 q^{27} - 28 q^{28} - 92 q^{29} - 120 q^{30} - 218 q^{31} - 96 q^{32} - 132 q^{33} + 168 q^{34} - 282 q^{35} - 108 q^{36} + 490 q^{37} - 74 q^{38} + 54 q^{39} - 80 q^{40} + 688 q^{41} + 42 q^{42} + 103 q^{43} + 176 q^{44} + 180 q^{45} - 8 q^{46} - 322 q^{47} + 144 q^{48} - 1508 q^{49} - 332 q^{50} - 252 q^{51} + 36 q^{52} + 1322 q^{53} + 162 q^{54} + 248 q^{55} + 112 q^{56} + 111 q^{57} + 368 q^{58} - 252 q^{59} + 120 q^{60} + 435 q^{61} + 218 q^{62} - 63 q^{63} + 384 q^{64} - 3164 q^{65} - 264 q^{66} + 719 q^{67} - 672 q^{68} + 12 q^{69} - 564 q^{70} + 62 q^{71} - 216 q^{72} + 581 q^{73} - 490 q^{74} + 498 q^{75} + 20 q^{76} - 408 q^{77} - 54 q^{78} + 489 q^{79} - 160 q^{80} - 243 q^{81} + 1376 q^{82} + 4992 q^{83} - 168 q^{84} - 1632 q^{85} + 206 q^{86} - 552 q^{87} - 704 q^{88} - 1584 q^{89} - 180 q^{90} + 1573 q^{91} + 8 q^{92} - 327 q^{93} + 1288 q^{94} + 2362 q^{95} - 576 q^{96} - 974 q^{97} + 1508 q^{98} + 396 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 1.50000 2.59808i 0.288675 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) −2.09405 + 3.62701i −0.187298 + 0.324409i −0.944348 0.328947i \(-0.893306\pi\)
0.757051 + 0.653356i \(0.226640\pi\)
\(6\) 3.00000 + 5.19615i 0.204124 + 0.353553i
\(7\) 3.18810 0.172141 0.0860707 0.996289i \(-0.472569\pi\)
0.0860707 + 0.996289i \(0.472569\pi\)
\(8\) 8.00000 0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −4.18810 7.25401i −0.132440 0.229392i
\(11\) 69.4003 1.90227 0.951135 0.308774i \(-0.0999187\pi\)
0.951135 + 0.308774i \(0.0999187\pi\)
\(12\) −12.0000 −0.288675
\(13\) 4.06431 + 7.03960i 0.0867106 + 0.150187i 0.906119 0.423023i \(-0.139031\pi\)
−0.819408 + 0.573210i \(0.805698\pi\)
\(14\) −3.18810 + 5.52196i −0.0608612 + 0.105415i
\(15\) 6.28216 + 10.8810i 0.108136 + 0.187298i
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 53.0418 91.8711i 0.756737 1.31071i −0.187770 0.982213i \(-0.560126\pi\)
0.944506 0.328493i \(-0.106541\pi\)
\(18\) 18.0000 0.235702
\(19\) 42.6656 70.9834i 0.515166 0.857090i
\(20\) 16.7524 0.187298
\(21\) 4.78216 8.28294i 0.0496930 0.0860707i
\(22\) −69.4003 + 120.205i −0.672554 + 1.16490i
\(23\) 88.2468 + 152.848i 0.800031 + 1.38570i 0.919595 + 0.392869i \(0.128517\pi\)
−0.119563 + 0.992827i \(0.538149\pi\)
\(24\) 12.0000 20.7846i 0.102062 0.176777i
\(25\) 53.7299 + 93.0629i 0.429839 + 0.744503i
\(26\) −16.2573 −0.122627
\(27\) −27.0000 −0.192450
\(28\) −6.37621 11.0439i −0.0430354 0.0745394i
\(29\) 33.1109 + 57.3498i 0.212019 + 0.367227i 0.952346 0.305019i \(-0.0986628\pi\)
−0.740327 + 0.672247i \(0.765330\pi\)
\(30\) −25.1286 −0.152928
\(31\) −140.915 −0.816421 −0.408210 0.912888i \(-0.633847\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 104.100 180.307i 0.549138 0.951135i
\(34\) 106.084 + 183.742i 0.535094 + 0.926809i
\(35\) −6.67606 + 11.5633i −0.0322417 + 0.0558443i
\(36\) −18.0000 + 31.1769i −0.0833333 + 0.144338i
\(37\) −156.003 −0.693156 −0.346578 0.938021i \(-0.612656\pi\)
−0.346578 + 0.938021i \(0.612656\pi\)
\(38\) 80.2814 + 144.882i 0.342720 + 0.618501i
\(39\) 24.3859 0.100125
\(40\) −16.7524 + 29.0160i −0.0662198 + 0.114696i
\(41\) 207.281 359.022i 0.789559 1.36756i −0.136679 0.990615i \(-0.543643\pi\)
0.926238 0.376940i \(-0.123024\pi\)
\(42\) 9.56431 + 16.5659i 0.0351382 + 0.0608612i
\(43\) −57.9252 + 100.329i −0.205430 + 0.355816i −0.950270 0.311428i \(-0.899193\pi\)
0.744839 + 0.667244i \(0.232526\pi\)
\(44\) −138.801 240.410i −0.475568 0.823707i
\(45\) 37.6929 0.124865
\(46\) −352.987 −1.13142
\(47\) −310.141 537.181i −0.962527 1.66715i −0.716117 0.697980i \(-0.754082\pi\)
−0.246410 0.969166i \(-0.579251\pi\)
\(48\) 24.0000 + 41.5692i 0.0721688 + 0.125000i
\(49\) −332.836 −0.970367
\(50\) −214.920 −0.607884
\(51\) −159.125 275.613i −0.436902 0.756737i
\(52\) 16.2573 28.1584i 0.0433553 0.0750936i
\(53\) 185.993 + 322.149i 0.482039 + 0.834916i 0.999787 0.0206167i \(-0.00656296\pi\)
−0.517748 + 0.855533i \(0.673230\pi\)
\(54\) 27.0000 46.7654i 0.0680414 0.117851i
\(55\) −145.328 + 251.715i −0.356291 + 0.617114i
\(56\) 25.5048 0.0608612
\(57\) −120.422 217.324i −0.279830 0.505004i
\(58\) −132.444 −0.299840
\(59\) −45.8465 + 79.4084i −0.101164 + 0.175222i −0.912165 0.409824i \(-0.865590\pi\)
0.811000 + 0.585046i \(0.198923\pi\)
\(60\) 25.1286 43.5241i 0.0540682 0.0936489i
\(61\) −109.310 189.331i −0.229438 0.397399i 0.728203 0.685361i \(-0.240356\pi\)
−0.957642 + 0.287962i \(0.907022\pi\)
\(62\) 140.915 244.072i 0.288648 0.499954i
\(63\) −14.3465 24.8488i −0.0286902 0.0496930i
\(64\) 64.0000 0.125000
\(65\) −34.0436 −0.0649628
\(66\) 208.201 + 360.615i 0.388299 + 0.672554i
\(67\) 72.6712 + 125.870i 0.132510 + 0.229515i 0.924644 0.380833i \(-0.124363\pi\)
−0.792133 + 0.610348i \(0.791030\pi\)
\(68\) −424.334 −0.756737
\(69\) 529.481 0.923797
\(70\) −13.3521 23.1265i −0.0227983 0.0394879i
\(71\) −443.915 + 768.883i −0.742014 + 1.28521i 0.209563 + 0.977795i \(0.432796\pi\)
−0.951577 + 0.307410i \(0.900538\pi\)
\(72\) −36.0000 62.3538i −0.0589256 0.102062i
\(73\) −99.5081 + 172.353i −0.159542 + 0.276334i −0.934703 0.355429i \(-0.884335\pi\)
0.775162 + 0.631763i \(0.217668\pi\)
\(74\) 156.003 270.205i 0.245067 0.424469i
\(75\) 322.379 0.496335
\(76\) −331.225 5.83100i −0.499923 0.00880082i
\(77\) 221.255 0.327460
\(78\) −24.3859 + 42.2376i −0.0353995 + 0.0613137i
\(79\) 194.779 337.367i 0.277397 0.480465i −0.693340 0.720610i \(-0.743862\pi\)
0.970737 + 0.240145i \(0.0771951\pi\)
\(80\) −33.5048 58.0321i −0.0468244 0.0811023i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 414.563 + 718.044i 0.558302 + 0.967008i
\(83\) 380.039 0.502586 0.251293 0.967911i \(-0.419144\pi\)
0.251293 + 0.967911i \(0.419144\pi\)
\(84\) −38.2573 −0.0496930
\(85\) 222.145 + 384.766i 0.283470 + 0.490985i
\(86\) −115.850 200.659i −0.145261 0.251600i
\(87\) 198.666 0.244818
\(88\) 555.202 0.672554
\(89\) 212.899 + 368.753i 0.253565 + 0.439188i 0.964505 0.264065i \(-0.0850635\pi\)
−0.710940 + 0.703253i \(0.751730\pi\)
\(90\) −37.6929 + 65.2861i −0.0441465 + 0.0764640i
\(91\) 12.9575 + 22.4430i 0.0149265 + 0.0258534i
\(92\) 352.987 611.392i 0.400016 0.692848i
\(93\) −211.372 + 366.107i −0.235680 + 0.408210i
\(94\) 1240.57 1.36122
\(95\) 168.113 + 303.391i 0.181559 + 0.327656i
\(96\) −96.0000 −0.102062
\(97\) −209.923 + 363.597i −0.219736 + 0.380595i −0.954727 0.297482i \(-0.903853\pi\)
0.734991 + 0.678077i \(0.237186\pi\)
\(98\) 332.836 576.489i 0.343077 0.594226i
\(99\) −312.301 540.922i −0.317045 0.549138i
\(100\) 214.920 372.252i 0.214920 0.372252i
\(101\) 620.855 + 1075.35i 0.611657 + 1.05942i 0.990961 + 0.134150i \(0.0428302\pi\)
−0.379304 + 0.925272i \(0.623836\pi\)
\(102\) 636.501 0.617873
\(103\) −593.606 −0.567862 −0.283931 0.958845i \(-0.591639\pi\)
−0.283931 + 0.958845i \(0.591639\pi\)
\(104\) 32.5145 + 56.3168i 0.0306568 + 0.0530992i
\(105\) 20.0282 + 34.6898i 0.0186148 + 0.0322417i
\(106\) −743.971 −0.681706
\(107\) −1778.56 −1.60691 −0.803457 0.595363i \(-0.797008\pi\)
−0.803457 + 0.595363i \(0.797008\pi\)
\(108\) 54.0000 + 93.5307i 0.0481125 + 0.0833333i
\(109\) 534.995 926.639i 0.470121 0.814274i −0.529295 0.848438i \(-0.677543\pi\)
0.999416 + 0.0341638i \(0.0108768\pi\)
\(110\) −290.656 503.431i −0.251936 0.436366i
\(111\) −234.005 + 405.308i −0.200097 + 0.346578i
\(112\) −25.5048 + 44.1757i −0.0215177 + 0.0372697i
\(113\) 583.197 0.485510 0.242755 0.970088i \(-0.421949\pi\)
0.242755 + 0.970088i \(0.421949\pi\)
\(114\) 496.837 + 8.74651i 0.408185 + 0.00718584i
\(115\) −739.173 −0.599376
\(116\) 132.444 229.399i 0.106009 0.183614i
\(117\) 36.5788 63.3564i 0.0289035 0.0500624i
\(118\) −91.6929 158.817i −0.0715341 0.123901i
\(119\) 169.103 292.895i 0.130266 0.225627i
\(120\) 50.2573 + 87.0481i 0.0382320 + 0.0662198i
\(121\) 3485.40 2.61863
\(122\) 437.241 0.324475
\(123\) −621.844 1077.07i −0.455852 0.789559i
\(124\) 281.830 + 488.143i 0.204105 + 0.353521i
\(125\) −973.566 −0.696627
\(126\) 57.3859 0.0405741
\(127\) −829.677 1437.04i −0.579700 1.00407i −0.995513 0.0946199i \(-0.969836\pi\)
0.415814 0.909450i \(-0.363497\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) 173.776 + 300.988i 0.118605 + 0.205430i
\(130\) 34.0436 58.9652i 0.0229678 0.0397814i
\(131\) −298.773 + 517.490i −0.199267 + 0.345140i −0.948291 0.317403i \(-0.897189\pi\)
0.749024 + 0.662543i \(0.230523\pi\)
\(132\) −832.804 −0.549138
\(133\) 136.022 226.303i 0.0886814 0.147541i
\(134\) −290.685 −0.187398
\(135\) 56.5394 97.9291i 0.0360455 0.0624326i
\(136\) 424.334 734.969i 0.267547 0.463405i
\(137\) 888.654 + 1539.19i 0.554182 + 0.959871i 0.997967 + 0.0637373i \(0.0203020\pi\)
−0.443785 + 0.896133i \(0.646365\pi\)
\(138\) −529.481 + 917.087i −0.326611 + 0.565708i
\(139\) −81.7836 141.653i −0.0499050 0.0864379i 0.839994 0.542596i \(-0.182559\pi\)
−0.889899 + 0.456158i \(0.849225\pi\)
\(140\) 53.4085 0.0322417
\(141\) −1860.85 −1.11143
\(142\) −887.829 1537.77i −0.524683 0.908778i
\(143\) 282.065 + 488.550i 0.164947 + 0.285697i
\(144\) 144.000 0.0833333
\(145\) −277.344 −0.158843
\(146\) −199.016 344.706i −0.112813 0.195398i
\(147\) −499.254 + 864.733i −0.280121 + 0.485184i
\(148\) 312.006 + 540.411i 0.173289 + 0.300145i
\(149\) 559.899 969.774i 0.307844 0.533201i −0.670047 0.742319i \(-0.733726\pi\)
0.977890 + 0.209118i \(0.0670592\pi\)
\(150\) −322.379 + 558.377i −0.175481 + 0.303942i
\(151\) −2807.15 −1.51286 −0.756432 0.654073i \(-0.773059\pi\)
−0.756432 + 0.654073i \(0.773059\pi\)
\(152\) 341.325 567.868i 0.182139 0.303027i
\(153\) −954.752 −0.504491
\(154\) −221.255 + 383.226i −0.115774 + 0.200527i
\(155\) 295.083 511.099i 0.152914 0.264854i
\(156\) −48.7718 84.4752i −0.0250312 0.0433553i
\(157\) −501.971 + 869.439i −0.255170 + 0.441967i −0.964942 0.262465i \(-0.915465\pi\)
0.709772 + 0.704432i \(0.248798\pi\)
\(158\) 389.558 + 674.734i 0.196149 + 0.339740i
\(159\) 1115.96 0.556611
\(160\) 134.019 0.0662198
\(161\) 281.340 + 487.295i 0.137719 + 0.238536i
\(162\) −81.0000 140.296i −0.0392837 0.0680414i
\(163\) 1271.99 0.611225 0.305612 0.952156i \(-0.401139\pi\)
0.305612 + 0.952156i \(0.401139\pi\)
\(164\) −1658.25 −0.789559
\(165\) 435.984 + 755.146i 0.205705 + 0.356291i
\(166\) −380.039 + 658.246i −0.177691 + 0.307770i
\(167\) 1492.49 + 2585.07i 0.691572 + 1.19784i 0.971323 + 0.237765i \(0.0764149\pi\)
−0.279751 + 0.960073i \(0.590252\pi\)
\(168\) 38.2573 66.2635i 0.0175691 0.0304306i
\(169\) 1065.46 1845.44i 0.484963 0.839980i
\(170\) −888.578 −0.400887
\(171\) −745.256 13.1198i −0.333282 0.00586721i
\(172\) 463.402 0.205430
\(173\) −28.3873 + 49.1683i −0.0124754 + 0.0216081i −0.872196 0.489157i \(-0.837304\pi\)
0.859720 + 0.510765i \(0.170638\pi\)
\(174\) −198.666 + 344.099i −0.0865563 + 0.149920i
\(175\) 171.297 + 296.694i 0.0739931 + 0.128160i
\(176\) −555.202 + 961.639i −0.237784 + 0.411854i
\(177\) 137.539 + 238.225i 0.0584073 + 0.101164i
\(178\) −851.598 −0.358595
\(179\) −4640.98 −1.93790 −0.968948 0.247266i \(-0.920468\pi\)
−0.968948 + 0.247266i \(0.920468\pi\)
\(180\) −75.3859 130.572i −0.0312163 0.0540682i
\(181\) −1887.70 3269.60i −0.775204 1.34269i −0.934680 0.355491i \(-0.884314\pi\)
0.159476 0.987202i \(-0.449020\pi\)
\(182\) −51.8298 −0.0211093
\(183\) −655.862 −0.264933
\(184\) 705.974 + 1222.78i 0.282854 + 0.489917i
\(185\) 326.679 565.824i 0.129826 0.224866i
\(186\) −422.744 732.215i −0.166651 0.288648i
\(187\) 3681.12 6375.88i 1.43952 2.49332i
\(188\) −1240.57 + 2148.72i −0.481264 + 0.833573i
\(189\) −86.0788 −0.0331286
\(190\) −693.603 12.2104i −0.264838 0.00466230i
\(191\) −2762.53 −1.04654 −0.523271 0.852166i \(-0.675288\pi\)
−0.523271 + 0.852166i \(0.675288\pi\)
\(192\) 96.0000 166.277i 0.0360844 0.0625000i
\(193\) −1030.76 + 1785.32i −0.384433 + 0.665857i −0.991690 0.128648i \(-0.958936\pi\)
0.607258 + 0.794505i \(0.292270\pi\)
\(194\) −419.846 727.194i −0.155377 0.269121i
\(195\) −51.0653 + 88.4477i −0.0187531 + 0.0324814i
\(196\) 665.672 + 1152.98i 0.242592 + 0.420181i
\(197\) 2094.82 0.757614 0.378807 0.925476i \(-0.376334\pi\)
0.378807 + 0.925476i \(0.376334\pi\)
\(198\) 1249.21 0.448370
\(199\) 858.681 + 1487.28i 0.305881 + 0.529801i 0.977457 0.211134i \(-0.0677158\pi\)
−0.671576 + 0.740935i \(0.734382\pi\)
\(200\) 429.839 + 744.503i 0.151971 + 0.263222i
\(201\) 436.027 0.153010
\(202\) −2483.42 −0.865014
\(203\) 105.561 + 182.837i 0.0364972 + 0.0632151i
\(204\) −636.501 + 1102.45i −0.218451 + 0.378368i
\(205\) 868.116 + 1503.62i 0.295765 + 0.512280i
\(206\) 593.606 1028.16i 0.200769 0.347743i
\(207\) 794.221 1375.63i 0.266677 0.461898i
\(208\) −130.058 −0.0433553
\(209\) 2961.00 4926.27i 0.979985 1.63042i
\(210\) −80.1127 −0.0263252
\(211\) 1145.53 1984.11i 0.373750 0.647354i −0.616389 0.787442i \(-0.711405\pi\)
0.990139 + 0.140088i \(0.0447384\pi\)
\(212\) 743.971 1288.60i 0.241020 0.417458i
\(213\) 1331.74 + 2306.65i 0.428402 + 0.742014i
\(214\) 1778.56 3080.55i 0.568130 0.984030i
\(215\) −242.597 420.190i −0.0769533 0.133287i
\(216\) −216.000 −0.0680414
\(217\) −449.251 −0.140540
\(218\) 1069.99 + 1853.28i 0.332426 + 0.575779i
\(219\) 298.524 + 517.059i 0.0921114 + 0.159542i
\(220\) 1162.62 0.356291
\(221\) 862.314 0.262468
\(222\) −468.009 810.616i −0.141490 0.245067i
\(223\) −1628.09 + 2819.94i −0.488902 + 0.846804i −0.999918 0.0127673i \(-0.995936\pi\)
0.511016 + 0.859571i \(0.329269\pi\)
\(224\) −51.0097 88.3514i −0.0152153 0.0263537i
\(225\) 483.569 837.566i 0.143280 0.248168i
\(226\) −583.197 + 1010.13i −0.171654 + 0.297313i
\(227\) −998.044 −0.291817 −0.145909 0.989298i \(-0.546611\pi\)
−0.145909 + 0.989298i \(0.546611\pi\)
\(228\) −511.987 + 851.801i −0.148716 + 0.247421i
\(229\) −1028.59 −0.296816 −0.148408 0.988926i \(-0.547415\pi\)
−0.148408 + 0.988926i \(0.547415\pi\)
\(230\) 739.173 1280.29i 0.211912 0.367042i
\(231\) 331.883 574.838i 0.0945295 0.163730i
\(232\) 264.887 + 458.799i 0.0749600 + 0.129835i
\(233\) 62.7431 108.674i 0.0176414 0.0305557i −0.857070 0.515200i \(-0.827718\pi\)
0.874711 + 0.484644i \(0.161051\pi\)
\(234\) 73.1577 + 126.713i 0.0204379 + 0.0353995i
\(235\) 2597.81 0.721117
\(236\) 366.772 0.101164
\(237\) −584.337 1012.10i −0.160155 0.277397i
\(238\) 338.206 + 585.789i 0.0921118 + 0.159542i
\(239\) 3591.03 0.971901 0.485950 0.873986i \(-0.338474\pi\)
0.485950 + 0.873986i \(0.338474\pi\)
\(240\) −201.029 −0.0540682
\(241\) 1845.92 + 3197.23i 0.493386 + 0.854570i 0.999971 0.00762002i \(-0.00242555\pi\)
−0.506585 + 0.862190i \(0.669092\pi\)
\(242\) −3485.40 + 6036.89i −0.925827 + 1.60358i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) −437.241 + 757.324i −0.114719 + 0.198700i
\(245\) 696.976 1207.20i 0.181748 0.314796i
\(246\) 2487.38 0.644672
\(247\) 673.101 + 11.8495i 0.173394 + 0.00305250i
\(248\) −1127.32 −0.288648
\(249\) 570.058 987.369i 0.145084 0.251293i
\(250\) 973.566 1686.27i 0.246295 0.426595i
\(251\) −3647.44 6317.55i −0.917228 1.58869i −0.803606 0.595162i \(-0.797088\pi\)
−0.113622 0.993524i \(-0.536245\pi\)
\(252\) −57.3859 + 99.3953i −0.0143451 + 0.0248465i
\(253\) 6124.35 + 10607.7i 1.52188 + 2.63597i
\(254\) 3318.71 0.819820
\(255\) 1332.87 0.327323
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) −1151.60 1994.63i −0.279513 0.484131i 0.691751 0.722136i \(-0.256840\pi\)
−0.971264 + 0.238006i \(0.923506\pi\)
\(258\) −695.102 −0.167733
\(259\) −497.354 −0.119321
\(260\) 68.0871 + 117.930i 0.0162407 + 0.0281297i
\(261\) 297.998 516.148i 0.0706730 0.122409i
\(262\) −597.546 1034.98i −0.140903 0.244051i
\(263\) −3569.19 + 6182.01i −0.836827 + 1.44943i 0.0557070 + 0.998447i \(0.482259\pi\)
−0.892534 + 0.450980i \(0.851075\pi\)
\(264\) 832.804 1442.46i 0.194150 0.336277i
\(265\) −1557.91 −0.361139
\(266\) 255.945 + 461.900i 0.0589963 + 0.106470i
\(267\) 1277.40 0.292792
\(268\) 290.685 503.481i 0.0662552 0.114757i
\(269\) 2723.33 4716.95i 0.617265 1.06913i −0.372717 0.927945i \(-0.621574\pi\)
0.989983 0.141190i \(-0.0450928\pi\)
\(270\) 113.079 + 195.858i 0.0254880 + 0.0441465i
\(271\) 1701.84 2947.67i 0.381474 0.660732i −0.609799 0.792556i \(-0.708750\pi\)
0.991273 + 0.131824i \(0.0420834\pi\)
\(272\) 848.669 + 1469.94i 0.189184 + 0.327677i
\(273\) 77.7448 0.0172356
\(274\) −3554.62 −0.783731
\(275\) 3728.87 + 6458.59i 0.817670 + 1.41625i
\(276\) −1058.96 1834.17i −0.230949 0.400016i
\(277\) −5131.93 −1.11317 −0.556584 0.830791i \(-0.687888\pi\)
−0.556584 + 0.830791i \(0.687888\pi\)
\(278\) 327.134 0.0705763
\(279\) 634.117 + 1098.32i 0.136070 + 0.235680i
\(280\) −53.4085 + 92.5062i −0.0113992 + 0.0197439i
\(281\) −1683.34 2915.63i −0.357365 0.618975i 0.630154 0.776470i \(-0.282992\pi\)
−0.987520 + 0.157495i \(0.949658\pi\)
\(282\) 1860.85 3223.08i 0.392950 0.680609i
\(283\) −3342.88 + 5790.04i −0.702168 + 1.21619i 0.265535 + 0.964101i \(0.414451\pi\)
−0.967704 + 0.252090i \(0.918882\pi\)
\(284\) 3551.32 0.742014
\(285\) 1040.40 + 18.3156i 0.216239 + 0.00380675i
\(286\) −1128.26 −0.233270
\(287\) 660.835 1144.60i 0.135916 0.235413i
\(288\) −144.000 + 249.415i −0.0294628 + 0.0510310i
\(289\) −3170.36 5491.23i −0.645301 1.11769i
\(290\) 277.344 480.374i 0.0561593 0.0972708i
\(291\) 629.768 + 1090.79i 0.126865 + 0.219736i
\(292\) 796.065 0.159542
\(293\) −5625.93 −1.12174 −0.560871 0.827903i \(-0.689534\pi\)
−0.560871 + 0.827903i \(0.689534\pi\)
\(294\) −998.508 1729.47i −0.198075 0.343077i
\(295\) −192.010 332.571i −0.0378957 0.0656374i
\(296\) −1248.02 −0.245067
\(297\) −1873.81 −0.366092
\(298\) 1119.80 + 1939.55i 0.217678 + 0.377030i
\(299\) −717.325 + 1242.44i −0.138742 + 0.240309i
\(300\) −644.759 1116.75i −0.124084 0.214920i
\(301\) −184.672 + 319.861i −0.0353631 + 0.0612507i
\(302\) 2807.15 4862.12i 0.534878 0.926436i
\(303\) 3725.13 0.706281
\(304\) 642.251 + 1159.06i 0.121170 + 0.218673i
\(305\) 915.606 0.171893
\(306\) 954.752 1653.68i 0.178365 0.308936i
\(307\) −2801.77 + 4852.81i −0.520865 + 0.902164i 0.478841 + 0.877902i \(0.341057\pi\)
−0.999706 + 0.0242627i \(0.992276\pi\)
\(308\) −442.511 766.451i −0.0818649 0.141794i
\(309\) −890.409 + 1542.23i −0.163928 + 0.283931i
\(310\) 590.166 + 1022.20i 0.108126 + 0.187280i
\(311\) 6668.20 1.21582 0.607908 0.794008i \(-0.292009\pi\)
0.607908 + 0.794008i \(0.292009\pi\)
\(312\) 195.087 0.0353995
\(313\) −2245.70 3889.67i −0.405541 0.702418i 0.588843 0.808247i \(-0.299584\pi\)
−0.994384 + 0.105829i \(0.966250\pi\)
\(314\) −1003.94 1738.88i −0.180432 0.312518i
\(315\) 120.169 0.0214945
\(316\) −1558.23 −0.277397
\(317\) 633.023 + 1096.43i 0.112158 + 0.194264i 0.916640 0.399713i \(-0.130890\pi\)
−0.804482 + 0.593977i \(0.797557\pi\)
\(318\) −1115.96 + 1932.89i −0.196792 + 0.340853i
\(319\) 2297.91 + 3980.10i 0.403317 + 0.698566i
\(320\) −134.019 + 232.128i −0.0234122 + 0.0405512i
\(321\) −2667.84 + 4620.83i −0.463876 + 0.803457i
\(322\) −1125.36 −0.194764
\(323\) −4258.27 7684.82i −0.733549 1.32382i
\(324\) 324.000 0.0555556
\(325\) −436.750 + 756.474i −0.0745432 + 0.129113i
\(326\) −1271.99 + 2203.14i −0.216101 + 0.374297i
\(327\) −1604.99 2779.92i −0.271425 0.470121i
\(328\) 1658.25 2872.17i 0.279151 0.483504i
\(329\) −988.763 1712.59i −0.165691 0.286985i
\(330\) −1743.93 −0.290910
\(331\) −5068.09 −0.841594 −0.420797 0.907155i \(-0.638249\pi\)
−0.420797 + 0.907155i \(0.638249\pi\)
\(332\) −760.077 1316.49i −0.125647 0.217626i
\(333\) 702.014 + 1215.92i 0.115526 + 0.200097i
\(334\) −5969.97 −0.978031
\(335\) −608.709 −0.0992757
\(336\) 76.5145 + 132.527i 0.0124232 + 0.0215177i
\(337\) −5372.06 + 9304.68i −0.868352 + 1.50403i −0.00467268 + 0.999989i \(0.501487\pi\)
−0.863680 + 0.504041i \(0.831846\pi\)
\(338\) 2130.93 + 3690.87i 0.342920 + 0.593955i
\(339\) 874.796 1515.19i 0.140155 0.242755i
\(340\) 888.578 1539.06i 0.141735 0.245492i
\(341\) −9779.53 −1.55305
\(342\) 767.980 1277.70i 0.121426 0.202018i
\(343\) −2154.64 −0.339182
\(344\) −463.402 + 802.635i −0.0726306 + 0.125800i
\(345\) −1108.76 + 1920.43i −0.173025 + 0.299688i
\(346\) −56.7747 98.3367i −0.00882146 0.0152792i
\(347\) 2425.67 4201.38i 0.375264 0.649977i −0.615102 0.788447i \(-0.710885\pi\)
0.990367 + 0.138471i \(0.0442186\pi\)
\(348\) −397.331 688.198i −0.0612046 0.106009i
\(349\) −7611.35 −1.16741 −0.583705 0.811966i \(-0.698398\pi\)
−0.583705 + 0.811966i \(0.698398\pi\)
\(350\) −685.186 −0.104642
\(351\) −109.736 190.069i −0.0166875 0.0289035i
\(352\) −1110.40 1923.28i −0.168139 0.291225i
\(353\) 5567.64 0.839477 0.419739 0.907645i \(-0.362122\pi\)
0.419739 + 0.907645i \(0.362122\pi\)
\(354\) −550.158 −0.0826004
\(355\) −1859.16 3220.16i −0.277955 0.481432i
\(356\) 851.598 1475.01i 0.126783 0.219594i
\(357\) −507.308 878.684i −0.0752090 0.130266i
\(358\) 4640.98 8038.42i 0.685149 1.18671i
\(359\) −2170.66 + 3759.69i −0.319116 + 0.552726i −0.980304 0.197495i \(-0.936719\pi\)
0.661187 + 0.750221i \(0.270053\pi\)
\(360\) 301.544 0.0441465
\(361\) −3218.30 6057.10i −0.469208 0.883088i
\(362\) 7550.82 1.09630
\(363\) 5228.10 9055.34i 0.755935 1.30932i
\(364\) 51.8298 89.7719i 0.00746325 0.0129267i
\(365\) −416.750 721.833i −0.0597636 0.103514i
\(366\) 655.862 1135.99i 0.0936679 0.162238i
\(367\) 4482.24 + 7763.47i 0.637524 + 1.10422i 0.985974 + 0.166896i \(0.0533745\pi\)
−0.348451 + 0.937327i \(0.613292\pi\)
\(368\) −2823.90 −0.400016
\(369\) −3731.06 −0.526372
\(370\) 653.357 + 1131.65i 0.0918012 + 0.159004i
\(371\) 592.965 + 1027.04i 0.0829789 + 0.143724i
\(372\) 1690.98 0.235680
\(373\) 5048.11 0.700755 0.350377 0.936609i \(-0.386053\pi\)
0.350377 + 0.936609i \(0.386053\pi\)
\(374\) 7362.23 + 12751.8i 1.01789 + 1.76304i
\(375\) −1460.35 + 2529.40i −0.201099 + 0.348314i
\(376\) −2481.13 4297.45i −0.340305 0.589425i
\(377\) −269.147 + 466.175i −0.0367686 + 0.0636850i
\(378\) 86.0788 149.093i 0.0117127 0.0202871i
\(379\) −9290.41 −1.25915 −0.629573 0.776941i \(-0.716770\pi\)
−0.629573 + 0.776941i \(0.716770\pi\)
\(380\) 714.752 1189.14i 0.0964894 0.160531i
\(381\) −4978.06 −0.669380
\(382\) 2762.53 4784.84i 0.370009 0.640874i
\(383\) −2081.13 + 3604.62i −0.277652 + 0.480907i −0.970801 0.239887i \(-0.922890\pi\)
0.693149 + 0.720794i \(0.256223\pi\)
\(384\) 192.000 + 332.554i 0.0255155 + 0.0441942i
\(385\) −463.320 + 802.495i −0.0613325 + 0.106231i
\(386\) −2061.51 3570.65i −0.271835 0.470832i
\(387\) 1042.65 0.136954
\(388\) 1679.38 0.219736
\(389\) −2092.61 3624.51i −0.272750 0.472417i 0.696815 0.717251i \(-0.254600\pi\)
−0.969565 + 0.244834i \(0.921267\pi\)
\(390\) −102.131 176.895i −0.0132605 0.0229678i
\(391\) 18723.1 2.42165
\(392\) −2662.69 −0.343077
\(393\) 896.320 + 1552.47i 0.115047 + 0.199267i
\(394\) −2094.82 + 3628.34i −0.267857 + 0.463942i
\(395\) 815.754 + 1412.93i 0.103912 + 0.179980i
\(396\) −1249.21 + 2163.69i −0.158523 + 0.274569i
\(397\) 2264.88 3922.89i 0.286325 0.495930i −0.686605 0.727031i \(-0.740900\pi\)
0.972930 + 0.231101i \(0.0742329\pi\)
\(398\) −3434.72 −0.432581
\(399\) −383.918 692.850i −0.0481703 0.0869321i
\(400\) −1719.36 −0.214920
\(401\) 4748.53 8224.69i 0.591347 1.02424i −0.402704 0.915330i \(-0.631930\pi\)
0.994051 0.108913i \(-0.0347370\pi\)
\(402\) −436.027 + 755.221i −0.0540972 + 0.0936991i
\(403\) −572.722 991.984i −0.0707924 0.122616i
\(404\) 2483.42 4301.41i 0.305829 0.529711i
\(405\) −169.618 293.787i −0.0208109 0.0360455i
\(406\) −422.245 −0.0516149
\(407\) −10826.7 −1.31857
\(408\) −1273.00 2204.91i −0.154468 0.267547i
\(409\) 2677.22 + 4637.08i 0.323667 + 0.560608i 0.981242 0.192781i \(-0.0617508\pi\)
−0.657574 + 0.753390i \(0.728417\pi\)
\(410\) −3472.46 −0.418275
\(411\) 5331.93 0.639914
\(412\) 1187.21 + 2056.31i 0.141965 + 0.245891i
\(413\) −146.163 + 253.162i −0.0174146 + 0.0301630i
\(414\) 1588.44 + 2751.26i 0.188569 + 0.326611i
\(415\) −795.821 + 1378.40i −0.0941333 + 0.163044i
\(416\) 130.058 225.267i 0.0153284 0.0265496i
\(417\) −490.701 −0.0576253
\(418\) 5571.55 + 10054.9i 0.651946 + 1.17656i
\(419\) 14506.1 1.69134 0.845668 0.533709i \(-0.179202\pi\)
0.845668 + 0.533709i \(0.179202\pi\)
\(420\) 80.1127 138.759i 0.00930738 0.0161209i
\(421\) 631.724 1094.18i 0.0731315 0.126667i −0.827141 0.561995i \(-0.810034\pi\)
0.900272 + 0.435327i \(0.143367\pi\)
\(422\) 2291.05 + 3968.22i 0.264281 + 0.457749i
\(423\) −2791.27 + 4834.63i −0.320842 + 0.555715i
\(424\) 1487.94 + 2577.19i 0.170427 + 0.295187i
\(425\) 11399.7 1.30110
\(426\) −5326.98 −0.605852
\(427\) −348.493 603.607i −0.0394959 0.0684089i
\(428\) 3557.12 + 6161.11i 0.401729 + 0.695814i
\(429\) 1692.39 0.190464
\(430\) 970.387 0.108828
\(431\) 4093.81 + 7090.69i 0.457522 + 0.792451i 0.998829 0.0483738i \(-0.0154039\pi\)
−0.541308 + 0.840825i \(0.682071\pi\)
\(432\) 216.000 374.123i 0.0240563 0.0416667i
\(433\) 4621.47 + 8004.63i 0.512919 + 0.888401i 0.999888 + 0.0149820i \(0.00476910\pi\)
−0.486969 + 0.873419i \(0.661898\pi\)
\(434\) 449.251 778.126i 0.0496884 0.0860628i
\(435\) −416.016 + 720.561i −0.0458539 + 0.0794213i
\(436\) −4279.96 −0.470121
\(437\) 14614.8 + 257.284i 1.59982 + 0.0281637i
\(438\) −1194.10 −0.130265
\(439\) 1021.52 1769.33i 0.111059 0.192359i −0.805139 0.593086i \(-0.797909\pi\)
0.916197 + 0.400727i \(0.131243\pi\)
\(440\) −1162.62 + 2013.72i −0.125968 + 0.218183i
\(441\) 1497.76 + 2594.20i 0.161728 + 0.280121i
\(442\) −862.314 + 1493.57i −0.0927966 + 0.160728i
\(443\) 4834.57 + 8373.71i 0.518504 + 0.898075i 0.999769 + 0.0214998i \(0.00684413\pi\)
−0.481265 + 0.876575i \(0.659823\pi\)
\(444\) 1872.04 0.200097
\(445\) −1783.29 −0.189969
\(446\) −3256.19 5639.88i −0.345706 0.598781i
\(447\) −1679.70 2909.32i −0.177734 0.307844i
\(448\) 204.039 0.0215177
\(449\) −13227.2 −1.39027 −0.695134 0.718881i \(-0.744655\pi\)
−0.695134 + 0.718881i \(0.744655\pi\)
\(450\) 967.138 + 1675.13i 0.101314 + 0.175481i
\(451\) 14385.4 24916.2i 1.50195 2.60146i
\(452\) −1166.39 2020.26i −0.121377 0.210232i
\(453\) −4210.72 + 7293.18i −0.436726 + 0.756432i
\(454\) 998.044 1728.66i 0.103173 0.178701i
\(455\) −108.534 −0.0111828
\(456\) −963.376 1738.59i −0.0989347 0.178546i
\(457\) −5380.98 −0.550791 −0.275396 0.961331i \(-0.588809\pi\)
−0.275396 + 0.961331i \(0.588809\pi\)
\(458\) 1028.59 1781.56i 0.104940 0.181762i
\(459\) −1432.13 + 2480.52i −0.145634 + 0.252246i
\(460\) 1478.35 + 2560.57i 0.149844 + 0.259538i
\(461\) 1422.33 2463.55i 0.143698 0.248892i −0.785189 0.619257i \(-0.787434\pi\)
0.928886 + 0.370365i \(0.120767\pi\)
\(462\) 663.766 + 1149.68i 0.0668424 + 0.115774i
\(463\) 6625.39 0.665028 0.332514 0.943098i \(-0.392103\pi\)
0.332514 + 0.943098i \(0.392103\pi\)
\(464\) −1059.55 −0.106009
\(465\) −885.249 1533.30i −0.0882848 0.152914i
\(466\) 125.486 + 217.348i 0.0124743 + 0.0216062i
\(467\) −18635.1 −1.84653 −0.923264 0.384167i \(-0.874489\pi\)
−0.923264 + 0.384167i \(0.874489\pi\)
\(468\) −292.631 −0.0289035
\(469\) 231.683 + 401.288i 0.0228106 + 0.0395090i
\(470\) −2597.81 + 4499.54i −0.254953 + 0.441592i
\(471\) 1505.91 + 2608.32i 0.147322 + 0.255170i
\(472\) −366.772 + 635.267i −0.0357670 + 0.0619503i
\(473\) −4020.03 + 6962.89i −0.390784 + 0.676858i
\(474\) 2337.35 0.226493
\(475\) 8898.34 + 156.650i 0.859545 + 0.0151317i
\(476\) −1352.82 −0.130266
\(477\) 1673.94 2899.34i 0.160680 0.278305i
\(478\) −3591.03 + 6219.84i −0.343619 + 0.595165i
\(479\) −778.310 1348.07i −0.0742420 0.128591i 0.826514 0.562916i \(-0.190320\pi\)
−0.900756 + 0.434325i \(0.856987\pi\)
\(480\) 201.029 348.192i 0.0191160 0.0331099i
\(481\) −634.046 1098.20i −0.0601039 0.104103i
\(482\) −7383.68 −0.697754
\(483\) 1688.04 0.159024
\(484\) −6970.80 12073.8i −0.654659 1.13390i
\(485\) −879.179 1522.78i −0.0823123 0.142569i
\(486\) −486.000 −0.0453609
\(487\) 19339.5 1.79950 0.899751 0.436405i \(-0.143748\pi\)
0.899751 + 0.436405i \(0.143748\pi\)
\(488\) −874.482 1514.65i −0.0811188 0.140502i
\(489\) 1907.98 3304.72i 0.176445 0.305612i
\(490\) 1393.95 + 2414.40i 0.128515 + 0.222594i
\(491\) 3419.12 5922.10i 0.314262 0.544319i −0.665018 0.746827i \(-0.731576\pi\)
0.979280 + 0.202509i \(0.0649095\pi\)
\(492\) −2487.38 + 4308.26i −0.227926 + 0.394779i
\(493\) 7025.05 0.641770
\(494\) −693.625 + 1154.00i −0.0631734 + 0.105103i
\(495\) 2615.90 0.237527
\(496\) 1127.32 1952.57i 0.102053 0.176760i
\(497\) −1415.25 + 2451.28i −0.127731 + 0.221237i
\(498\) 1140.12 + 1974.74i 0.102590 + 0.177691i
\(499\) 9057.49 15688.0i 0.812563 1.40740i −0.0985021 0.995137i \(-0.531405\pi\)
0.911065 0.412263i \(-0.135262\pi\)
\(500\) 1947.13 + 3372.53i 0.174157 + 0.301648i
\(501\) 8954.95 0.798559
\(502\) 14589.8 1.29716
\(503\) 2915.92 + 5050.53i 0.258478 + 0.447698i 0.965834 0.259160i \(-0.0834456\pi\)
−0.707356 + 0.706857i \(0.750112\pi\)
\(504\) −114.772 198.791i −0.0101435 0.0175691i
\(505\) −5200.41 −0.458248
\(506\) −24497.4 −2.15226
\(507\) −3196.39 5536.31i −0.279993 0.484963i
\(508\) −3318.71 + 5748.17i −0.289850 + 0.502035i
\(509\) −4957.32 8586.34i −0.431689 0.747707i 0.565330 0.824865i \(-0.308749\pi\)
−0.997019 + 0.0771579i \(0.975415\pi\)
\(510\) −1332.87 + 2308.59i −0.115726 + 0.200444i
\(511\) −317.242 + 549.480i −0.0274637 + 0.0475686i
\(512\) 512.000 0.0441942
\(513\) −1151.97 + 1916.55i −0.0991437 + 0.164947i
\(514\) 4606.40 0.395291
\(515\) 1243.04 2153.01i 0.106359 0.184220i
\(516\) 695.102 1203.95i 0.0593027 0.102715i
\(517\) −21523.9 37280.5i −1.83099 3.17136i
\(518\) 497.354 861.443i 0.0421863 0.0730688i
\(519\) 85.1620 + 147.505i 0.00720269 + 0.0124754i
\(520\) −272.348 −0.0229678
\(521\) −5851.91 −0.492086 −0.246043 0.969259i \(-0.579131\pi\)
−0.246043 + 0.969259i \(0.579131\pi\)
\(522\) 595.997 + 1032.30i 0.0499733 + 0.0865563i
\(523\) −3447.05 5970.46i −0.288200 0.499178i 0.685180 0.728374i \(-0.259724\pi\)
−0.973380 + 0.229196i \(0.926390\pi\)
\(524\) 2390.19 0.199267
\(525\) 1027.78 0.0854399
\(526\) −7138.38 12364.0i −0.591726 1.02490i
\(527\) −7474.37 + 12946.0i −0.617816 + 1.07009i
\(528\) 1665.61 + 2884.92i 0.137285 + 0.237784i
\(529\) −9491.49 + 16439.7i −0.780101 + 1.35117i
\(530\) 1557.91 2698.39i 0.127682 0.221152i
\(531\) 825.236 0.0674430
\(532\) −1055.98 18.5899i −0.0860574 0.00151499i
\(533\) 3369.83 0.273853
\(534\) −1277.40 + 2212.52i −0.103518 + 0.179298i
\(535\) 3724.40 6450.84i 0.300971 0.521298i
\(536\) 581.370 + 1006.96i 0.0468495 + 0.0811458i
\(537\) −6961.47 + 12057.6i −0.559422 + 0.968948i
\(538\) 5446.66 + 9433.89i 0.436472 + 0.755992i
\(539\) −23098.9 −1.84590
\(540\) −452.315 −0.0360455
\(541\) 2812.50 + 4871.39i 0.223509 + 0.387130i 0.955871 0.293786i \(-0.0949153\pi\)
−0.732362 + 0.680916i \(0.761582\pi\)
\(542\) 3403.68 + 5895.34i 0.269743 + 0.467208i
\(543\) −11326.2 −0.895129
\(544\) −3394.67 −0.267547
\(545\) 2240.62 + 3880.86i 0.176105 + 0.305023i
\(546\) −77.7448 + 134.658i −0.00609372 + 0.0105546i
\(547\) −1798.07 3114.35i −0.140548 0.243437i 0.787155 0.616755i \(-0.211553\pi\)
−0.927703 + 0.373319i \(0.878220\pi\)
\(548\) 3554.62 6156.78i 0.277091 0.479935i
\(549\) −983.793 + 1703.98i −0.0764795 + 0.132466i
\(550\) −14915.5 −1.15636
\(551\) 5483.59 + 96.5350i 0.423972 + 0.00746376i
\(552\) 4235.85 0.326611
\(553\) 620.975 1075.56i 0.0477515 0.0827080i
\(554\) 5131.93 8888.76i 0.393564 0.681674i
\(555\) −980.036 1697.47i −0.0749553 0.129826i
\(556\) −327.134 + 566.613i −0.0249525 + 0.0432190i
\(557\) −9190.73 15918.8i −0.699145 1.21095i −0.968763 0.247987i \(-0.920231\pi\)
0.269618 0.962967i \(-0.413103\pi\)
\(558\) −2536.47 −0.192432
\(559\) −941.705 −0.0712520
\(560\) −106.817 185.012i −0.00806043 0.0139611i
\(561\) −11043.3 19127.6i −0.831106 1.43952i
\(562\) 6733.36 0.505391
\(563\) 5578.33 0.417582 0.208791 0.977960i \(-0.433047\pi\)
0.208791 + 0.977960i \(0.433047\pi\)
\(564\) 3721.70 + 6446.17i 0.277858 + 0.481264i
\(565\) −1221.25 + 2115.26i −0.0909349 + 0.157504i
\(566\) −6685.76 11580.1i −0.496508 0.859977i
\(567\) −129.118 + 223.639i −0.00956342 + 0.0165643i
\(568\) −3551.32 + 6151.06i −0.262341 + 0.454389i
\(569\) 16981.3 1.25113 0.625564 0.780173i \(-0.284869\pi\)
0.625564 + 0.780173i \(0.284869\pi\)
\(570\) −1072.13 + 1783.72i −0.0787833 + 0.131073i
\(571\) −19520.5 −1.43066 −0.715332 0.698785i \(-0.753724\pi\)
−0.715332 + 0.698785i \(0.753724\pi\)
\(572\) 1128.26 1954.20i 0.0824735 0.142848i
\(573\) −4143.79 + 7177.26i −0.302111 + 0.523271i
\(574\) 1321.67 + 2289.20i 0.0961070 + 0.166462i
\(575\) −9482.98 + 16425.0i −0.687770 + 1.19125i
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) 6371.35 0.459693 0.229846 0.973227i \(-0.426178\pi\)
0.229846 + 0.973227i \(0.426178\pi\)
\(578\) 12681.4 0.912593
\(579\) 3092.27 + 5355.97i 0.221952 + 0.384433i
\(580\) 554.688 + 960.748i 0.0397107 + 0.0687809i
\(581\) 1211.60 0.0865159
\(582\) −2519.07 −0.179414
\(583\) 12908.0 + 22357.2i 0.916969 + 1.58824i
\(584\) −796.065 + 1378.82i −0.0564065 + 0.0976989i
\(585\) 153.196 + 265.343i 0.0108271 + 0.0187531i
\(586\) 5625.93 9744.39i 0.396596 0.686924i
\(587\) −5379.52 + 9317.61i −0.378257 + 0.655160i −0.990809 0.135271i \(-0.956810\pi\)
0.612552 + 0.790430i \(0.290143\pi\)
\(588\) 3994.03 0.280121
\(589\) −6012.21 + 10002.6i −0.420592 + 0.699747i
\(590\) 768.039 0.0535927
\(591\) 3142.23 5442.51i 0.218704 0.378807i
\(592\) 1248.02 2161.64i 0.0866444 0.150073i
\(593\) −1805.88 3127.87i −0.125057 0.216604i 0.796698 0.604377i \(-0.206578\pi\)
−0.921755 + 0.387773i \(0.873245\pi\)
\(594\) 1873.81 3245.53i 0.129433 0.224185i
\(595\) 708.220 + 1226.67i 0.0487970 + 0.0845188i
\(596\) −4479.19 −0.307844
\(597\) 5152.09 0.353201
\(598\) −1434.65 2484.89i −0.0981057 0.169924i
\(599\) 4590.12 + 7950.31i 0.313100 + 0.542306i 0.979032 0.203707i \(-0.0652991\pi\)
−0.665932 + 0.746013i \(0.731966\pi\)
\(600\) 2579.03 0.175481
\(601\) 12700.4 0.862000 0.431000 0.902352i \(-0.358161\pi\)
0.431000 + 0.902352i \(0.358161\pi\)
\(602\) −369.343 639.721i −0.0250055 0.0433108i
\(603\) 654.041 1132.83i 0.0441702 0.0765050i
\(604\) 5614.29 + 9724.24i 0.378216 + 0.655089i
\(605\) −7298.61 + 12641.6i −0.490464 + 0.849509i
\(606\) −3725.13 + 6452.12i −0.249708 + 0.432507i
\(607\) −24227.5 −1.62004 −0.810019 0.586404i \(-0.800543\pi\)
−0.810019 + 0.586404i \(0.800543\pi\)
\(608\) −2649.80 46.6480i −0.176749 0.00311156i
\(609\) 633.367 0.0421434
\(610\) −915.606 + 1585.88i −0.0607734 + 0.105263i
\(611\) 2521.02 4366.54i 0.166923 0.289119i
\(612\) 1909.50 + 3307.36i 0.126123 + 0.218451i
\(613\) 8106.74 14041.3i 0.534141 0.925159i −0.465064 0.885277i \(-0.653969\pi\)
0.999204 0.0398814i \(-0.0126980\pi\)
\(614\) −5603.54 9705.62i −0.368307 0.637927i
\(615\) 5208.70 0.341520
\(616\) 1770.04 0.115774
\(617\) 10757.7 + 18632.8i 0.701924 + 1.21577i 0.967790 + 0.251758i \(0.0810087\pi\)
−0.265866 + 0.964010i \(0.585658\pi\)
\(618\) −1780.82 3084.47i −0.115914 0.200769i
\(619\) −15878.5 −1.03103 −0.515516 0.856880i \(-0.672400\pi\)
−0.515516 + 0.856880i \(0.672400\pi\)
\(620\) −2360.66 −0.152914
\(621\) −2382.66 4126.89i −0.153966 0.266677i
\(622\) −6668.20 + 11549.7i −0.429856 + 0.744532i
\(623\) 678.746 + 1175.62i 0.0436491 + 0.0756024i
\(624\) −195.087 + 337.901i −0.0125156 + 0.0216777i
\(625\) −4677.54 + 8101.73i −0.299362 + 0.518511i
\(626\) 8982.80 0.573522
\(627\) −8357.32 15082.3i −0.532312 0.960654i
\(628\) 4015.77 0.255170
\(629\) −8274.68 + 14332.2i −0.524536 + 0.908523i
\(630\) −120.169 + 208.139i −0.00759944 + 0.0131626i
\(631\) −2779.87 4814.88i −0.175380 0.303768i 0.764912 0.644134i \(-0.222782\pi\)
−0.940293 + 0.340366i \(0.889449\pi\)
\(632\) 1558.23 2698.94i 0.0980745 0.169870i
\(633\) −3436.58 5952.33i −0.215785 0.373750i
\(634\) −2532.09 −0.158616
\(635\) 6949.55 0.434306
\(636\) −2231.91 3865.79i −0.139153 0.241020i
\(637\) −1352.75 2343.03i −0.0841412 0.145737i
\(638\) −9191.64 −0.570377
\(639\) 7990.46 0.494676
\(640\) −268.039 464.257i −0.0165549 0.0286740i
\(641\) 10243.5 17742.2i 0.631190 1.09325i −0.356119 0.934441i \(-0.615900\pi\)
0.987309 0.158812i \(-0.0507665\pi\)
\(642\) −5335.68 9241.66i −0.328010 0.568130i
\(643\) 2051.15 3552.69i 0.125800 0.217892i −0.796245 0.604974i \(-0.793184\pi\)
0.922045 + 0.387082i \(0.126517\pi\)
\(644\) 1125.36 1949.18i 0.0688593 0.119268i
\(645\) −1455.58 −0.0888580
\(646\) 17568.8 + 309.287i 1.07002 + 0.0188370i
\(647\) 22860.4 1.38908 0.694539 0.719455i \(-0.255608\pi\)
0.694539 + 0.719455i \(0.255608\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) −3181.76 + 5510.97i −0.192442 + 0.333320i
\(650\) −873.501 1512.95i −0.0527100 0.0912964i
\(651\) −673.877 + 1167.19i −0.0405704 + 0.0702700i
\(652\) −2543.97 4406.29i −0.152806 0.264668i
\(653\) 26388.5 1.58141 0.790706 0.612197i \(-0.209714\pi\)
0.790706 + 0.612197i \(0.209714\pi\)
\(654\) 6419.94 0.383853
\(655\) −1251.29 2167.30i −0.0746444 0.129288i
\(656\) 3316.50 + 5744.35i 0.197390 + 0.341889i
\(657\) 1791.15 0.106361
\(658\) 3955.05 0.234322
\(659\) −1611.65 2791.45i −0.0952668 0.165007i 0.814453 0.580229i \(-0.197037\pi\)
−0.909720 + 0.415222i \(0.863704\pi\)
\(660\) 1743.93 3020.58i 0.102852 0.178146i
\(661\) 13740.1 + 23798.5i 0.808513 + 1.40039i 0.913894 + 0.405953i \(0.133060\pi\)
−0.105381 + 0.994432i \(0.533606\pi\)
\(662\) 5068.09 8778.19i 0.297548 0.515369i
\(663\) 1293.47 2240.36i 0.0757681 0.131234i
\(664\) 3040.31 0.177691
\(665\) 535.963 + 967.243i 0.0312538 + 0.0564031i
\(666\) −2808.06 −0.163378
\(667\) −5843.87 + 10121.9i −0.339244 + 0.587587i
\(668\) 5969.97 10340.3i 0.345786 0.598919i
\(669\) 4884.28 + 8459.82i 0.282268 + 0.488902i
\(670\) 608.709 1054.32i 0.0350992 0.0607937i
\(671\) −7586.17 13139.6i −0.436454 0.755961i
\(672\) −306.058 −0.0175691
\(673\) −2165.00 −0.124004 −0.0620020 0.998076i \(-0.519749\pi\)
−0.0620020 + 0.998076i \(0.519749\pi\)
\(674\) −10744.1 18609.4i −0.614018 1.06351i
\(675\) −1450.71 2512.70i −0.0827226 0.143280i
\(676\) −8523.70 −0.484963
\(677\) 11999.0 0.681179 0.340589 0.940212i \(-0.389373\pi\)
0.340589 + 0.940212i \(0.389373\pi\)
\(678\) 1749.59 + 3030.38i 0.0991043 + 0.171654i
\(679\) −669.256 + 1159.19i −0.0378258 + 0.0655161i
\(680\) 1777.16 + 3078.13i 0.100222 + 0.173589i
\(681\) −1497.07 + 2593.00i −0.0842404 + 0.145909i
\(682\) 9779.53 16938.6i 0.549087 0.951047i
\(683\) 5234.35 0.293246 0.146623 0.989192i \(-0.453160\pi\)
0.146623 + 0.989192i \(0.453160\pi\)
\(684\) 1445.06 + 2607.88i 0.0807798 + 0.145782i
\(685\) −7443.56 −0.415188
\(686\) 2154.64 3731.94i 0.119919 0.207706i
\(687\) −1542.88 + 2672.34i −0.0856834 + 0.148408i
\(688\) −926.803 1605.27i −0.0513576 0.0889540i
\(689\) −1511.87 + 2618.63i −0.0835958 + 0.144792i
\(690\) −2217.52 3840.86i −0.122347 0.211912i
\(691\) −5160.63 −0.284109 −0.142055 0.989859i \(-0.545371\pi\)
−0.142055 + 0.989859i \(0.545371\pi\)
\(692\) 227.099 0.0124754
\(693\) −995.649 1724.52i −0.0545766 0.0945295i
\(694\) 4851.34 + 8402.76i 0.265352 + 0.459603i
\(695\) 685.036 0.0373884
\(696\) 1589.32 0.0865563
\(697\) −21989.1 38086.3i −1.19498 2.06976i
\(698\) 7611.35 13183.2i 0.412742 0.714890i
\(699\) −188.229 326.023i −0.0101852 0.0176414i
\(700\) 685.186 1186.78i 0.0369966 0.0640799i
\(701\) 1657.51 2870.90i 0.0893059 0.154682i −0.817912 0.575343i \(-0.804868\pi\)
0.907218 + 0.420661i \(0.138202\pi\)
\(702\) 438.946 0.0235996
\(703\) −6655.96 + 11073.6i −0.357090 + 0.594097i
\(704\) 4441.62 0.237784
\(705\) 3896.71 6749.31i 0.208168 0.360558i
\(706\) −5567.64 + 9643.43i −0.296800 + 0.514073i
\(707\) 1979.35 + 3428.34i 0.105292 + 0.182370i
\(708\) 550.158 952.901i 0.0292037 0.0505822i
\(709\) 9166.60 + 15877.0i 0.485555 + 0.841007i 0.999862 0.0165995i \(-0.00528404\pi\)
−0.514307 + 0.857606i \(0.671951\pi\)
\(710\) 7436.64 0.393088
\(711\) −3506.02 −0.184931
\(712\) 1703.20 + 2950.02i 0.0896488 + 0.155276i
\(713\) −12435.3 21538.5i −0.653162 1.13131i
\(714\) 2029.23 0.106362
\(715\) −2362.63 −0.123577
\(716\) 9281.96 + 16076.8i 0.484474 + 0.839133i
\(717\) 5386.54 9329.76i 0.280564 0.485950i
\(718\) −4341.31 7519.37i −0.225649 0.390836i
\(719\) −4873.50 + 8441.15i −0.252783 + 0.437833i −0.964291 0.264845i \(-0.914679\pi\)
0.711508 + 0.702678i \(0.248013\pi\)
\(720\) −301.544 + 522.289i −0.0156081 + 0.0270341i
\(721\) −1892.48 −0.0977526
\(722\) 13709.5 + 482.844i 0.706669 + 0.0248886i
\(723\) 11075.5 0.569713
\(724\) −7550.82 + 13078.4i −0.387602 + 0.671346i
\(725\) −3558.09 + 6162.80i −0.182268 + 0.315697i
\(726\) 10456.2 + 18110.7i 0.534526 + 0.925827i
\(727\) −16361.8 + 28339.4i −0.834697 + 1.44574i 0.0595791 + 0.998224i \(0.481024\pi\)
−0.894277 + 0.447515i \(0.852309\pi\)
\(728\) 103.660 + 179.544i 0.00527731 + 0.00914057i
\(729\) 729.000 0.0370370
\(730\) 1667.00 0.0845185
\(731\) 6144.91 + 10643.3i 0.310914 + 0.538518i
\(732\) 1311.72 + 2271.97i 0.0662332 + 0.114719i
\(733\) 36938.2 1.86131 0.930657 0.365894i \(-0.119237\pi\)
0.930657 + 0.365894i \(0.119237\pi\)
\(734\) −17929.0 −0.901594
\(735\) −2090.93 3621.59i −0.104932 0.181748i
\(736\) 2823.90 4891.13i 0.141427 0.244959i
\(737\) 5043.40 + 8735.43i 0.252071 + 0.436599i
\(738\) 3731.06 6462.39i 0.186101 0.322336i
\(739\) 4993.60 8649.16i 0.248569 0.430534i −0.714560 0.699574i \(-0.753373\pi\)
0.963129 + 0.269040i \(0.0867064\pi\)
\(740\) −2613.43 −0.129826
\(741\) 1040.44 1730.99i 0.0515809 0.0858160i
\(742\) −2371.86 −0.117350
\(743\) −10869.9 + 18827.2i −0.536713 + 0.929615i 0.462365 + 0.886690i \(0.347001\pi\)
−0.999078 + 0.0429249i \(0.986332\pi\)
\(744\) −1690.98 + 2928.86i −0.0833256 + 0.144324i
\(745\) 2344.92 + 4061.51i 0.115317 + 0.199735i
\(746\) −5048.11 + 8743.59i −0.247754 + 0.429123i
\(747\) −1710.17 2962.11i −0.0837644 0.145084i
\(748\) −29448.9 −1.43952
\(749\) −5670.23 −0.276617
\(750\) −2920.70 5058.80i −0.142198 0.246295i
\(751\) 19033.7 + 32967.3i 0.924833 + 1.60186i 0.791830 + 0.610742i \(0.209129\pi\)
0.133003 + 0.991116i \(0.457538\pi\)
\(752\) 9924.53 0.481264
\(753\) −21884.6 −1.05912
\(754\) −538.293 932.351i −0.0259993 0.0450321i
\(755\) 5878.31 10181.5i 0.283356 0.490787i
\(756\) 172.158 + 298.186i 0.00828216 + 0.0143451i
\(757\) 5682.61 9842.58i 0.272838 0.472569i −0.696750 0.717314i \(-0.745371\pi\)
0.969587 + 0.244746i \(0.0787045\pi\)
\(758\) 9290.41 16091.5i 0.445176 0.771067i
\(759\) 36746.1 1.75731
\(760\) 1344.91 + 2427.13i 0.0641907 + 0.115844i
\(761\) 24549.3 1.16940 0.584699 0.811250i \(-0.301213\pi\)
0.584699 + 0.811250i \(0.301213\pi\)
\(762\) 4978.06 8622.25i 0.236662 0.409910i
\(763\) 1705.62 2954.22i 0.0809274 0.140170i
\(764\) 5525.06 + 9569.68i 0.261636 + 0.453166i
\(765\) 1999.30 3462.89i 0.0944900 0.163662i
\(766\) −4162.26 7209.24i −0.196330 0.340053i
\(767\) −745.338 −0.0350881
\(768\) −768.000 −0.0360844
\(769\) −7111.27 12317.1i −0.333471 0.577588i 0.649719 0.760174i \(-0.274886\pi\)
−0.983190 + 0.182586i \(0.941553\pi\)
\(770\) −926.641 1604.99i −0.0433686 0.0751166i
\(771\) −6909.60 −0.322754
\(772\) 8246.06 0.384433
\(773\) −8041.29 13927.9i −0.374159 0.648063i 0.616041 0.787714i \(-0.288735\pi\)
−0.990201 + 0.139651i \(0.955402\pi\)
\(774\) −1042.65 + 1805.93i −0.0484204 + 0.0838666i